PDE-based tracking control for multi-agent deployment*

A two-degree-of-freedom control concept is developed for the deployment of multi-agent systems into desired formation profiles by exploiting a continuum model in terms of a modified viscous Burger's equation. For this, flatness-based motion planning and feedforward control is combined with a backstepping-based boundary controller to stabilise the distributed parameter tracking error system. An exogenous system is introduced, which is shown to enable translational movement of the complete formation as well as its separation and reunion. The transfer of the control strategy to a finite-dimensional discrete multi-agent system is obtained by proper discretization of the continuum model PDEs, which in addition imposes the required communication topology. The results are evaluated in different simulation scenarios for a leader-follower configuration.